]>PLB34119S03702693(18)30742110.1016/j.physletb.2018.09.041The AuthorsPhenomenologyFig. 1Feynman diagrams for the γn → K0Λ reaction.Fig. 1Fig. 2Change of the N⁎ spectrum from the 2010 edition of Review of Particle Physics to the 2012 edition.Fig. 2Fig. 3Left: Total cross section for the γn → K0Λ reaction as a function of the CM energy. The dashed (blue), dotdashed (magenta), and solid (black) curves correspond to contribution from K⁎ Reggeon exchange, that from the sum of N⁎ exchanges, and the total contribution, respectively. The data are taken from the CLAS experiment [26]. Right: Each contribution to the γn → K0Λ reaction for various nucleon resonances. (For interpretation of the colors in the figure(s), the reader is referred to the web version of this article.)Fig. 3Fig. 4Differential cross section for the γn → K0Λ reaction as a function of cosθCMK0 for each beam energy. The dashed (blue), dotdashed (magenta), and solid (black) curves correspond to the contribution from K⁎ Reggeon exchange, that from the sum of N⁎ exchanges, and the total contribution, respectively. The dotted (green) one indicates the total contribution without the effect of the narrow resonance N(1685,1/2+). The data are taken from the FOREST experiment [25].Fig. 4Fig. 5Differential cross section for the γn → K0Λ reaction as a function of cosθCMK0 for each beam energy. The notations are the same as in Fig. 4. The data are taken from the CLAS experiment [26].Fig. 5Fig. 6Differential cross section for γn → K0Λ as a function of W for each cosθCMK0. The notations are the same as Fig. 4. The data are taken from the CLAS experiment [26].Fig. 6Fig. 7Beam asymmetry Σγ→n→K0Λ as a function of cosθ for each beam energy when the nucleon resonances are not included (Left) and included (Right), respectively.Fig. 7Table 1The sixteen nucleon resonances listed by the Particle Data Group (PDG) [28] and information on their electromagnetic couplings. The helicity amplitudes A1/2,3/2 [10−3/GeV] are obtained from Ref. [28]. In addition, we introduce the narrow nucleon resonance in the last row of this table, which corresponds to the narrow enhancement in η photoproduction [1–6].Table 1StateRatingWidth [MeV]A1/2A3/2h1h2
N(1650,1/2−)****100–150(125)−50 ± 20 [36]⋯−0.31⋯
N(1675,5/2−)****130–160(145)−60 ± 5−85 ± 104.885.45
N(1680,5/2+)****100–135(120)≈30≈−35−7.448.57
N(1700,3/2−)***100–300(200)25 ± 10−32 ± 18−1.431.64
N(1710,1/2+)****80–200(140)−40 ± 20⋯0.24⋯
N(1720,3/2+)****150–400(250)−80 ± 50−140 ± 651.501.61
N(1860,5/2+)**30021 ± 1334 ± 170.281.09
N(1875,3/2−)***120–250(200)10 ± 6−20 ± 15−0.550.54
N(1880,1/2+)***200–400(300)−60 ± 50⋯0.31⋯
N(1895,1/2−)****80–200(120)13 ± 6⋯0.067⋯
N(1900,3/2+)****100–320(200)0 ± 30−60 ± 450.29−0.56
N(1990,7/2+)**100–320(200)−45 ± 20−52 ± 276.927.54
N(2000,5/2+)**300−18 ± 12−35 ± 20−0.47−0.56
N(2060,5/2−)***300–450(400)25 ± 11−37 ± 170.027−2.87
N(2120,3/2−)***260–360(300)110 ± 4540 ± 30−1.712.41
N(2190,7/2−)****300–500(400)−15 ± 13−34 ± 22−1.57−0.62

N(1685,1/2+)30−0.315 [37]
Table 2Information on the strong coupling constants of the nucleon resonances. The decay amplitudes G(ℓ) [MeV] are obtained from Ref. [38] and the branching ratios of N⁎s to the KΛ state are taken from Ref. [28].Table 2StateG(ℓ)gKΛN⁎ΓN⁎→KΛ/ΓN⁎[%]gKΛN⁎gKΛN⁎ (final)
N(1650,1/2−)−3.3 ± 1.0−0.785–150.59–1.02−0.78
N(1675,5/2−)0.4 ± 0.31.231.23
N(1680,5/2+)≃0.1 ± 0.1−2.84−2.84
N(1700,3/2−)−0.4 ± 0.32.342.34
N(1710,1/2+)4.7 ± 3.7−7.495–254.2–9.4−4.2
N(1720,3/2+)−3.2 ± 1.8−1.804–51.8–2.0−1.1
N(1860,5/2+)−0.5 ± 0.31.40seen1.40
N(1875,3/2−)≃1.7 ± 1.0−2.47seen−2.47
N(1880,1/2+)12–284.5–6.43.0
N(1895,1/2−)2.3 ± 2.70.3413–230.58–0.770.34
N(1900,3/2+)2–200.53–1.70.6
N(1990,7/2+)≃1.5 ± 2.40.610.61
N(2000,5/2+)−0.5 ± 0.30.610.61
N(2060,5/2−)≃−2.2 ± 1.0−0.52seen−0.52
N(2120,3/2−)≃1.7 ± 1.0−1.05−1.05
N(2190,7/2−)≃−1.10.670.67

N(1685,1/2+)−0.9
K0Λ photoproduction off the neutron with nucleon resonancesSangHoKimasangho.kim@apctp.orgHyunChulKimbcd⁎hchkim@inha.ac.kraAsia Pacific Center for Theoretical Physics (APCTP), Pohang 37673, Republic of KoreaAsia Pacific Center for Theoretical Physics (APCTP)Pohang37673Republic of KoreabDepartment of Physics, Inha University, Incheon 22212, Republic of KoreaDepartment of PhysicsInha UniversityIncheon22212Republic of KoreacAdvanced Science Research Center, Japan Atomic Energy Agency, Shirakata, Tokai, Ibaraki, 3191195, JapanAdvanced Science Research CenterJapan Atomic Energy AgencyShirakataTokaiIbaraki3191195JapandSchool of Physics, Korea Institute for Advanced Study (KIAS), Seoul 02455, Republic of KoreaSchool of PhysicsKorea Institute for Advanced Study (KIAS)Seoul02455Republic of Korea⁎Corresponding author.Editor: J.P. BlaizotAbstractWe investigate kaon photoproduction off the neutron target, i.e., γn→K0Λ, focusing on the role of nucleon resonances given in the Review of Particle Data Group in the range of s≈1600–2200 MeV. We employ an effective Lagrangian method and a Regge approach. The strong couplings of nucleon resonances with KΛ vertices are constrained by quark model predictions. The numerical results of the total and differential cross sections are found to be in qualitative agreement with the recent CLAS and FOREST experimental data. We discuss the effects of the narrow nucleon resonance N(1685,1/2+) on both the total and differential cross sections near the threshold energy. In addition, we present the results of the beam asymmetry as a prediction.KeywordsK0Λ photoproductionEffective Lagrangian approachtchannel Regge trajectoriesNucleon resonances1. Kuznetsov et al. reported the measurement of the cross sections for η photoproduction off the neutron, which shows a narrow bump structure near the centerofmass (CM) energy W=1.68 GeV [1]. In the γp→ηp reaction, there is only a small dip structure at the same energy. The LNSKEK Collaboration [2], the CBELSA and TAPS Collaborations in Bonn [3], and the A2 Collaboration in Mainz [4–6] have confirmed this feature of η photoproduction off the neutron. This phenomenon is often called the neutron anomaly in η photoproduction. However, there is no consensus in the interpretations on the narrow enhancement at W=1.68 GeV. In fact, the narrow nucleon resonance around 1.68 GeV was predicted by the chiral quarksoliton model [7–11] in which the neutron anomaly was explained in terms of the different values of the N(1685)→Nγ transition magnetic moments. The A2 measurement of the helicitydependent γn→ηn cross sections favors the existence of a narrow P11 resonance [4]. On the other hand, Ref. [12,13] disputed that such the narrow enhancement arises from the interference between N(1535,1/2−) and N(1650,1/2−), based on the Bonn–Gatchina multichannel partialwave analysis. However, Ref. [14] refuted it in favor of the narrow P11 nucleon resonance. In this situation it is of great importance to scrutinize the narrow structure around 1.68 GeV and the related neutron anomaly in other processes such as K0Λ photoproduction.In the present Letter, we investigate the K0Λ photoproduction off the neutron, focusing on the effects of the narrow resonance structure around 1.68 GeV, which appeared in the γn→ηn reaction. Since the threshold energy of the γn→K0Λ is 1.61 GeV, K0Λ photoproduction can provide a possible clue in understanding the nature of the narrow nucleon resonance N(1685,1/2+). In this regard, the investigation on K0Λ photoproduction will shed light on the neutron anomaly yet from the different facet. While the theoretical investigations of γn→ηn reaction have been carried out extensively in the literature [15–19], that of K0Λ photoproduction is very limited [20–23]. Recently, the FOREST Collaboration at the Research Center for Electron Photon Science, Tohoku University [24,25] and the CLAS Collaboration at the Thomas Jefferson National Accelerator Facility [26] have announced the experimental data on the total and differential cross sections of K0Λ photoproduction off the neutron.11However, one should keep in mind that both the experimental data from the CLAS and FOREST Collaborations were taken from the deuteron target, certain effects from the Fermi motion are involved in the course of extracting the twobody experimental data. Very recently, the beamtarget helicity asymmetry E is also measured at the CLAS Collaboration [27]. Thus, it is of great interest to examine theoretically the role of the narrow nucleon resonance N(1685,1/2+) also in this γn→K0Λ reaction. We will employ an effective Lagrangian approach in which we can consider directly the nucleon resonances in the s channel. We will introduce sixteen different nucleon resonances up to 2.2 GeV. In addition, we take into account the narrow nucleon resonance N(1685,1/2+) corresponding to the narrow enhancement found in η photoproduction off the neutron. We also include the K⁎ Reggeon exchange in the t channel, since it explains properly the highenergy behavior of the total cross section.2. In an effective Lagrangian approach, the γn→K0Λ reaction can be represented by the treelevel Feynman diagram illustrated in Fig. 1. The notations of the four momenta of the incoming and outgoing particles are given in Fig. 1(a) in which the tchannel K⁎ Reggeon exchange is depicted. Other exchanges such as K1(1270,1+),K1(1400,1+), and higher strange mesons are excluded in the present process because of their small photocouplings to the K0 meson, e.g., Br(K⁎(1410,1−)→K0γ)<2.2×10−4 [28].The schannel diagrams shown in Fig. 1(b) include contributions from the neutron and their resonances, generically. We will consider the sixteen different nucleon resonances taken from the Particle Data Group (PDG) data [28]. On top of them, we include the narrow resonance N(1685,1/2+), which corresponds to the narrow enhancement found in η photoproduction [1–6]. Λ and Σ exchanges are included in the uchannel diagrams drawn in Fig. 1(c).The general expressions of the electromagnetic (EM) interaction Lagrangians can be written as(1)LγKK⁎=gγKK⁎0ϵμναβ∂μAν(∂αK¯β⁎0K0+K¯0∂αKβ⁎0),LγNN=−N¯[eNγμ−eκN2MNσμν∂ν]AμN,LγΛΛ=eκΛ2MNΛ¯σμν∂νAμΛ,LγΣΛ=eμΣΛ2MNΣ¯0σμν∂νAμΛ+H.c., where Aμ, K, K⁎, and N designate the fields for the photon, pseudoscalar kaon, vector kaon, and nucleon, respectively. Λ and Σ denote respectively the fields for the groundstate hyperons. MN and eN stand respectively for the mass and electric charge of the nucleon, whereas e denotes the unit electric charge. Since the neutron is involved in the present work, we need only the magnetic term in the γNN vertex.Concerning the values of the coupling constants, gγKK⁎0 is determined by the experimental data for the decay width Γ(K⁎→Kγ), resulting in −0.388GeV−1 [28]. The sign of the coupling is fixed from the quark model. The anomalous and transition magnetic moments of the baryons are given by the PDG [28](2)κN=−1.91,κΛ=−0.61,μΣΛ=1.61.The effective Lagrangians for the mesonnucleonhyperon interactions are given by(3)LK⁎NΛ=−gK⁎NΛN¯[γμΛ−κK⁎NΛMN+MΛσμνΛ∂ν]K⁎μ+H.c.,LKNY=gKNYMN+MYN¯γμγ5Y∂μK+H.c., where Y represents generically the fields for the hyperons (Λ or Σ0). The strong coupling constants are taken from the average values of the Nijmegen softcore potential (NSC97) [29](4)gK⁎NΛ=−5.19,κK⁎NΛ=2.79,gKNΛ=−15.5,gKNΣ=4.70. Note that although we use the pseudovector coupling for the latter one in Eq. (3), the numerical results of the present work almost do not change when the pseudoscholar coupling is employed, since the effects of nucleon and hyperon exchanges turn out to be tiny.In general, the invariant amplitude for photoproduction can be written by(5)Mh=Ihu¯ΛMhμϵμuN, where ϵμ represents the polarization vector of the incident photon. uN and uΛ denote the Dirac spinors for the incoming nucleon and the outgoing Λ, respectively. The isospin factors are given by IK⁎=IN=IΛ=1 and IΣ=−1 in the present process. The effective Lagrangians of Eqs. (1) and (3) being considered, the individual amplitudes for the Born term are obtained as follows:(6)MK⁎μ=gγKK⁎0gK⁎NΛt−MK⁎2ϵμναβ[γν−iκK⁎NΛMN+MΛqtλσνλ]k1αk2β,MNμ=eκN2MNgKNΛ2MN1s−MN2γαγ5(/qs+MN)σμνk1νk2α,MΛμ=eκΛ2MNgKNΛMN+MΛ1u−MΛ2σμνk1ν(/qu+MΛ)γαγ5k2α,MΣμ=eμΣΛ2MNgKNΣMN+MΣ1u−MΣ2σμνk1ν(/qu+MΣ)γαγ5k2α, where qt,s,u designate the four momenta of the exchanged particles, i.e., qt=k2−k1, qs=k1+p1, and qu=p2−k1.Considering the finite sizes of hadrons, we need to introduce a form factor at each vertex. It is of course well known that certain ambiguities arise from the selection of hadronic form factors, in particular, when higher spin resonant baryons are involved [30,31]. Bearing in mind that most approaches based on effective Lagrangians inevitably contain uncertainties related to types of the form factors chosen, we will use the following generic type for the s and uchannel background diagrams(7)FB(q2)=[ΛB4ΛB4+(q2−MB2)2]2, where q2 denotes the squared momentum of qs,u and MB the mass of the corresponding exchanged baryon B, respectively. The form factor given in Eq. (7) tames sufficiently unphysically increasing cross sections as W increases. However, the gaussiantype form factors, which will be discussed after Eq. (20), are employed for higherspin baryon resonances, because they control more efficiently the resonance contributions such that the cross sections are regulated and the resonance structures are revealed reasonably well.Although we are mainly interested in the vicinity of the threshold energy for K0Λ photoproduction, future experiments are expected to cover higher energy regions. Thus, we employ the tchannel Regge trajectory for the K⁎meson exchange and follow Refs. [32,33]. This can be done by replacing the Feynman propagator in Eq. (6) with the Regge one as(8)1t−MK⁎2→PK⁎Regge(t)=(ss0)α(t)−1πα′sin[πα(t)]{1e−iπα(t)}1Γ[α(t)], where either a constant phase (1) or a rotating one (e−iπα(t)) can be considered for the Regge phase. The K⁎ Regge trajectory reads [33](9)α(t)=αK⁎(t)=0.83t+0.25, and α′≡∂α(t)/∂t denotes the slope parameter. The energyscale parameter is chosen to be s0=1GeV2 for simplicity. Consequently, the entire Born amplitude is written as(10)MBorn=MK⁎(t−MK⁎2)PK⁎Regge(t)+MnmagFn(s)+MΛFΛ(u)+MΣFΣ(u). Unlike the charged kaon production, all the terms are manifestly gaugeinvariant, so we do not need to introduce any prescription for gauge invariance.We also introduce N⁎ contributions in the s channel. Among the nucleon resonances listed in the PDG, we take into account sixteen different nucleon resonances in the range of s≈(1600–2200) MeV [28], including the narrow N(1685,1/2+) in addition. We first express the effective Lagrangians for the EM transitions of the nucleon resonances(11)LγNN⁎1/2±=eh12MNN¯Γ∓σμν∂νAμN⁎+H.c.,LγNN⁎3/2±=−ie[h12MNN¯Γν±−ih2(2MN)2∂νN¯Γ±]FμνNμ⁎+H.c.,LγNN⁎5/2±=e[h1(2MN)2N¯Γν∓−ih2(2MN)3∂νN¯Γ∓]∂αFμνNμα⁎+H.c.,LγNN⁎7/2±=ie[h1(2MN)3N¯Γν±−ih2(2MN)4∂νN¯Γ±]∂α∂βFμνNμαβ⁎+H.c., where the spin and parity are given in superscripts. N⁎, Nμ⁎, Nμα⁎, and Nμαβ⁎ stand for the spin1/2, 3/2, 5/2, and 7/2 nucleonresonance fields, respectively, with(12)Γ±=(γ5I4×4),Γν±=(γνγ5γν). hi designate the EM transition coupling constants and can be calculated from the Breit–Wigner helicity amplitudes Ai given in the PDG. We refer to Refs. [34,35] for the explicit relations between them. It is found that the values of the Ai for the 2018 edition of Review of Particle Physics [28] are almost the same as those for the 2016 edition [36] except for the N(1650,1/2−). It is changed from −50±20 to −10 [10−3/GeV]. We want to mention that we use the data on N(1650,1/2−) taken from the previous edition whereas those on excited nucleons are employed from the updated 2018 edition of PDG. All the relevant values are tabulated in Table 1, where we adopt the central values of Ai. The electromagnetic coupling of the narrow resonance N(1685,1/2+) is taken from Ref. [37]. As for the full decay width, the resonances less than 1800 MeV have rather small values (≃130 MeV) compared to those of the higher ones that give 200–400 MeV [28]. In the present numerical calculation, we use the values in parentheses in Table 1.The effective Lagrangians for the strong interactions are written as(13)LKΛN⁎1/2±=−igKΛN⁎K¯Λ¯Γ±N⁎+H.c.,LKΛN⁎3/2±=gKΛN⁎MK∂μK¯Λ¯Γ∓Nμ⁎+H.c.,LKΛN⁎5/2±=igKΛN⁎MK2∂μ∂νK¯Λ¯Γ±Nμν⁎+H.c.,LKΛN⁎7/2±=−gKΛN⁎MK3∂μ∂ν∂αK¯Λ¯Γ∓Nμνα⁎+H.c.. The strong coupling constants, gKΛN⁎, can be extracted from the quark model predictions where the information about the decay amplitude for the N⁎→KΛ decay is given [38]. They are related by the following relation [39]:(14)〈K(q→)Λ(−q→,mf)−iHintN⁎(0,mj)〉=4πMN⁎2q→∑ℓ,mℓ〈ℓmℓ12mfjmj〉Yℓ,mℓ(qˆ)G(ℓ), where 〈ℓmℓ12mfjmj〉 and Yℓ,mℓ(qˆ) are the Clebsch–Gordan coefficients and spherical harmonics, respectively. The decay width is then obtained from the partialwave decay amplitude G(ℓ)(15)Γ(N⁎→KΛ)=∑ℓG(ℓ)2. The spin and parity of the nucleon resonance impose constraints on the relative orbital angular momentum ℓ of the KΛ final state. In the case of a jP=12− resonance, the relative orbital angular momentum is restricted by the angular momentum conservation, so the s wave (ℓ=0) is only possible. Similarly, for the resonances of jP=(1/2+,3/2+), jP=(3/2−,5/2−), jP=(5/2+,7/2+), and jP=7/2−, the finalparticle states are in the relative p, d, f, and g waves, respectively. As a result, the relations between the decay amplitudes and the strong coupling constants for the decays of the jP=(1/2±,3/2±,5/2±,7/2±) resonances into the final state are derived as follows:(16)G(1+P2)=∓q→(EΛ∓MΛ)4πMN⁎gKΛN⁎forN⁎(1/2P),G(3−P2)=±q→3(EΛ±MΛ)12πMN⁎gKΛN⁎MKforN⁎(3/2P),G(5+P2)=∓q→5(EΛ∓MΛ)30πMN⁎gKΛN⁎MK2forN⁎(5/2P),G(7−P2)=±q→7(EΛ±MΛ)70πMN⁎gKΛN⁎MK3forN⁎(7/2P), where the magnitude of the threemomentum and the energy for the Λ in the rest frame of the resonance are given respectively as(17)q→=12MN⁎[MN⁎2−(MΛ+MK)2][MN⁎2−(MΛ−MK)2],EΛ=MΛ2+q→2.We should mention that the experimental data on the nucleon resonances in the 2012 edition of Review of Particle Physics [40] were much changed from those in the 2010 edition [41] (see Fig. 2). The JP=5/2+ state F15(2000) is split into N(1860,5/2+) and N(2000,5/2+), whereas the D13(2080) breaks up into N(1875,3/2−) and N(2120,3/2−). The S11(2090) is changed into N(1895,1/2−) and the N(2060,5/2−) was previously identified as D15(2200). Since the quark model predictions for the decay amplitudes [38] are obtained from the resonances before the 2012 edition of Review of Particle Physics, we thus make an assumption that the model values can be used for the corresponding revised resonances.It is worthwhile to compare these coupling constants extracted from the prediction of the quark model [38] with those calculated from the experimental data on the branching ratios [28], although the signs of the couplings can be fixed only in the quark models. In Table 2, we summarize both values for the seventeen different nucleon resonances under consideration. Only four resonances provide both of them. Comparing these two values, we find that they are close to each other. Since only the experimental data exist for the N(1880,1/2+) and N(1900,3/2+), we determine the strong coupling constants for them by using the PDG data. Their signs are determined phenomenologically. The last column in Table 2 shows the couplings gKΛN⁎ that are finally determined. They are mostly given within the range of the extracted coupling constants from the quark model predictions [38] or the PDG data [28]. Though we could reproduce the experimental data better by fitting the coupling constants, we have not performed it, because the main concern of the present work lies in understanding the role of each nucleon resonance and we want to avoid additional uncertainties arising from the values of the strong coupling constants.We can construct the individual amplitudes for the nucleonresonance exchange using Eqs. (11) and (13) in the form of M=IN⁎u¯ΛMN⁎uN as in Eq. (5) with IN⁎=1:(18)MN⁎1/2±=∓gKΛN⁎eh12MNΓ±(/qs+MN⁎)Γ∓s−MN⁎2+iMN⁎ΓN⁎σμνk1νϵμ,MN⁎3/2±=igKΛN⁎MKΓ∓k2μs−MN⁎2+iMN⁎ΓN⁎Δμρ(qs)×[eh12MNΓλ±∓eh2(2MN)2Γ±p1λ](k1ρϵλ−k1λϵρ),MN⁎5/2±=igKΛN⁎MK2Γ±k2μk2νs−MN⁎2+iMN⁎ΓN⁎Δμνρσ(qs)×[eh1(2MN)2Γλ∓±eh2(2MN)3Γ∓p1λ]k1σ(k1ρϵλ−k1λϵρ),MN⁎7/2±=igKΛN⁎MK3Γ∓k2μk2νk2αs−MN⁎2+iMN⁎ΓN⁎Δμναρσδ(qs)×[eh1(2MN)3Γλ±±eh2(2MN)4Γ±p1λ]×k1σk1δ(k1ρϵλ−k1λϵρ), where ΓN⁎ designates the full decay width of N⁎. The spin3/2, 5/2, and 7/2 projection operators, given by Δμρ, Δμνρσ, and Δμναρσδ, respectively, are represented in the Rarita–Schwinger formalism [42–45] as in Refs. [34,35,46,47]. The phase factors of the invariant amplitudes for the nucleon resonances cannot be determined by symmetries only, so we regard them as free parameters. These amplitudes are thus written by(19)MRes=∑N⁎eiψN⁎MN⁎FN⁎(s), where the gaussian form factor is employed [48,49](20)FN⁎(qs2)=exp{−(qs2−MN⁎2)2ΛN⁎4}.3. Before we present the numerical results, we need to mention how the model parameters are fixed. The cutoff masses are fixed to be ΛB(N,Λ,Σ),N⁎=0.9 GeV for simplicity. We do not fit the values of the cutoff masses to avoid additional uncertainties arising from them. We find that at high energies above the CM energy W=2.2GeV, where K⁎ Reggeon exchange comes into a dominant play, the rotating Regge phase (e−iπαK⁎(t)) and the phase angle ψN⁎=π turn out to be the best choice.In the left panel of Fig. 3, the total cross section for the γn→K0Λ reaction is drawn as a function of the CM energy. The N⁎ contributions are dominant in the lowerenergy region (W≲2.2 GeV). K⁎ Reggeon exchange in the t channel being included, the result is in agreement with the CLAS data [26]. As W increases, the K⁎ Reggeon takes over N⁎ contributions. Because of K⁎ Reggeon exchange, the total cross section behaves asymptotically as σ∼sαK⁎(0)−1 and describes the experimental data well. As shown in the left panel of Fig. 3, the result is slightly underestimated in the vicinity of the threshold energy, compared to the CLAS data. Each contribution of various nucleon resonances is drawn in the right panel of Fig. 3. The wellknown N(1650,1/2−) and N(1720,3/2+) are the most dominant ones. While the N(1675,5/2−), N(1710,1/2+), N(1880,1/2+), N(1900,3/2+), N(1990,7/2+), and N(2120,3/2−) have sizable effects on the total cross section, all other resonances almost do not affect it, so we show only the contributions of the nine nucleon resonances in the figure. Moreover, the N(1685,1/2+) resonance has only a marginal effect on the total cross section. Thus, as far as the results of the total cross section are concerned, the present ones are more or less similar to those of Ref. [50] where the Bonn–Gatchina coupledchannel partialwave analysis was used. In Ref. [50], it was shown that the partial waves JP=1/2± and 3/2+ contribute dominantly to the total cross section and the narrow bump structure is not seen unlike the γn→ηn cross section. However, the inclusion of the N(1685,1/2+) improves the data around W=1.68 GeV in the present calculation.Fig. 4 draws the differential cross sections for the γn→K0Λ reaction as a function of cosθCMK0, being compared with the FOREST experimental data [25]. The photon energy is varied from Eγ=937.5 MeV to Eγ=1137.5 MeV. The dashed curve is drawn for the contribution of K⁎ Reggeon exchange. As expected, its effect is rather small in the range of the photon energy given in Fig. 4. Here, main interest lies in the effect of the narrow resonance N(1685,1/2+). While the dotted curve is depicted without the N(1685,1/2+) taken into account, the solid one includes it. Though the effect of the N(1685,1/2+) is very small at smaller values of Eγ, it comes into play as Eγ increases. In particular, the experimental data of the differential cross section at Eγ=1037.5 MeV and Eγ=1062.5 MeV can be explained only by including the narrow resonance N(1685,1/2+). Otherwise, the results would be overestimated in the forward direction and would be underestimated in the backward direction. Although the N(1685,1/2+) does not give any significant contribution to the total cross section, it is essential to consider it to explain the differential cross section data in the range of the photon energies 1037MeV≤Eγ≤1062MeV.In Fig. 5, we compare the present results of the differential cross section with the CLAS data [26]. The CLAS experiment covers a much wider range of the photon energies (0.97GeV≤Eγ≤2.45GeV) than the FOREST experiment. The first three figures in the first row of Fig. 5 can be compared to the FOREST data given in Fig. 4. Though there are some discrepancies between these two experimental data, general tendency of the data is similar each other. The present results are also in qualitative agreement with the CLAS data. In particular, the narrow resonance N(1685,1/2+) pulls down the differential cross section at Eγ=1.05 GeV in the forward direction. On the other hand, the N(1685,1/2+) makes it enhanced in the backward direction, as we already discussed in Fig. 4. As a result, the inclusion of the N(1685,1/2+) provides noticeably better agreement with the data. As Eγ increases, i.e. Eγ≥1.8GeV (or W≥2.05GeV), the results are in good agreement with the CLAS data. This can be understood by K⁎ Reggeon exchange which governs the γn→K0Λ process in the higher energy region.We want to mention that we fit the value of the KΛN(1685) coupling constant to be gKΛN(1685,1/2+)=−(0.8–1.1), which implies the branching ratio Br(N(1685,1/2+)→KΛ)=(0.5–1.0)% with ΓN(1685,1/2+)=30 MeV. Consequently, we get the partial decay width ΓN⁎(1685)→KΛ to be (0.15–0.30) MeV, whereas another theoretical analysis based on the soliton picture yields 0.7(1.56) MeV for MN⁎=1680(1730) MeV [51]. We hope that future experiments may clarify these predictions. Meanwhile, Ref. [50] obtained the following upper limit(21)Br(N(1685)→KΛ)A1/2n<6×10−3GeV−1/2, which is consistent with our result, i.e., (3.7–5.2)×10−3GeV−1/2.We have fixed the mass of this narrow resonance to be MN⁎=1685 MeV. On the other hand, a simultaneous analysis of the γp→K+Λ and γn→K0Λ channels finds that the most appropriate mass is 1650 MeV [21,22]. The energies at Eγ=0.97 and 1.05 GeV in Fig. 5 correspond approximately to the energies at W=1650 and 1685 MeV, respectively. Thus, selecting such a low mass MN⁎=1650 MeV is not suitable to describe the CLAS data in our calculation, since the inclusion of the narrow resonance greatly improves the cross section result at the energy Eγ=1.05 GeV.Fig. 6 draws the differential cross sections for the γn→K0Λ reaction as a function of the CM energy with cosθCMK0 fixed. As in the case of Fig. 5, including the narrow resonance N(1685,1/2+) improves the description of the CLAS data near the threshold region [26]. In particular, the N(1685,1/2+) enhances the differential cross section in the backward angle, i.e. in the range of −0.7<cosθCMK0<0.0 around W=1.68 GeV. On the other hand, the N(1685,1/2+) makes it reduced in the forward direction. Yet another noticeable feature is that, by the inclusion of the N(1685,1/2+), destructive effects between it and other resonances begin to appear at the corresponding pole position as the angle cosθ increases as clearly seen in the last row of Fig. 6. This tendency is also shown in the CLAS data, especially in the g10 ones. This can strongly support the evidence of the existence of the narrow resonance N(1685,1/2+) in K0Λ photoproduction. One cannot explain these dip structures merely by adjusting the model parameters of other resonances.It is of great importance to examine the beam asymmetry and other polarization observables of K0Λ photoproduction both experimentally and theoretically, since they can clarify more clearly the role of nucleon resonances. In Fig. 7, we draw the predictions of the beam asymmetry Σγ→n→K0Λ as a function of cosθ for four different beam energies. The beam asymmetry is defined as follows:(22)Σγ→n→K0Λ=dσdΩ⊥−dσdΩ∥dσdΩ⊥+dσdΩ∥, where the subscript ⊥ means that the photon polarization vector is perpendicular to the reaction plane whereas ∥ denotes the parallel photon polarization to it. The left panel of Fig. 7 depicts the results of the beam asymmetry without the nucleon resonances. It shows that the beam asymmetry increases generally as cosθ increases. However, it falls off drastically in the very forward direction. If the photon energy Eγ increases, the magnitudes of the beam asymmetry become larger. On the other hand, when the nucleon resonances are included, the structure of the beam asymmetry is entirely changed. At Eγ=1.05 GeV, the cosθ dependence of Σγ is opposite to the case without the nucleon resonances, that is, when cosθ increases, the beam asymmetry increases till around cosθ=−0.3 and then slowly falls off. However, if one increase the photon energy, the results of Σγ are changed dramatically. One can understand this interesting feature of Σγ. Each contribution of the nucleon resonances depends on Eγ. As Eγ increases, higher lying nucleon resonances comes into play. It brings about the remarkable changes of the beam asymmetry.4. In the present work, we investigated K0Λ photoproduction, aiming at understanding the nature of the narrow resonance structure around 1.68 GeV. We employed an effective Lagrangian method combined with a Regge approach. We included seventeen different nucleon resonances in the s channel together with nucleon exchange as a background. In addition, we considered Λ and Σ exchanges the u channel. In the t channel, we included K⁎ Reggeon exchange which governs the behavior of the γn→K0Λ amplitude in higher energy regions. Since charged kaon photoproduction has been widely investigated in the literature, it is of great interest to compare the role of each diagram in both the charged and neutral productions. Even though the photocouplings are different, the important contributions in the s channel are similar to each other. For example, in Refs. [48,49,52–54], the N(1650,1/2−) and N(1720,3/2+) are the most significant ones and the N(1900,3/2+) is also required for the description of the cross section data.We have taken into account the nucleon resonances which appeared only in the PDG data. We were able to reproduce the recent CLAS and FOREST data reasonably well without any complicated fitting procedure, even though the nucleon resonances from the PDG data are considered only. The sign ambiguities of the strong coupling constants for the nucleon resonances were resolved by relating them to information on the partialwave decay amplitudes predicted by a quark model. We found that the narrow nucleon resonance N(1685,1/2+) has a certain contribution to the differential cross sections near the threshold energy. It enhances them in the backward direction while it makes them decreased in the forward direction, whereas it is difficult to see the effect of the N(1685,1/2+) on the total cross section. It is interesting to extend our approach to the study of KΣ photoproduction [55] and KΛ(KΣ) electroproduction [56]. Relevant works will appear elsewhere.AcknowledgementsAuthors are grateful to N. Compton for providing us with the CLAS experimental data. They want to express the gratitude to T. Ishikawa, Y. Tsuchikawa, H. Shimizu, Y. Oh, and Gh.S. Yang for fruitful discussions. H.Ch. K. is grateful to A. Hosaka, T. Maruyama, M. Oka for useful discussions. He wants to express his gratitude to the members of the Advanced Science Research Center at Japan Atomic Energy Agency for the hospitality, where part of the present work was done. S.H.K. acknowledges support by the Ministry of Science, ICT & Future Planning, Gyeongsangbukdo and Pohang City. This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2018R1A5A1025563).References[1]V.KuznetsovGRAAL CollaborationPhys. Lett. B647200723[2]F.MiyaharaProg. Theor. Phys. 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